A finite loop space not rationally equivalent to a compact Lie group
Algebraic Topology
2007-05-23 v1 Geometric Topology
Abstract
We construct a connected finite loop space of rank 66 and dimension 1254 whose rational cohomology is not isomorphic as a graded vector space to the rational cohomology of any compact Lie group, hence providing a counterexample to a classical conjecture. Aided by machine calculation we verify that our counterexample is minimal, i.e., that any finite loop space of rank less than 66 is in fact rationally equivalent to a compact Lie group, extending the classical known bound of 5.
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Cite
@article{arxiv.math/0306234,
title = {A finite loop space not rationally equivalent to a compact Lie group},
author = {Kasper K. S. Andersen and Tilman Bauer and Jesper Grodal and Erik K. Pedersen},
journal= {arXiv preprint arXiv:math/0306234},
year = {2007}
}
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8 pages